Earlier today, young Croatian defender Filip Benkovic became the sixth new arrival at the King Power Stadium after Jonny Evans, Ricardo Pereira, James Maddison, Rachid Ghezzal and Danny Ward.
"It is very good to have Harry back", he said.
United's need for a new centre-back is hardly a secret and according to reports they chased various players from Toby Alderweireld to Jerome Boateng.
However, despite discussions between the two clubs regarding the 25-year-old, who starred for England at this summer's World Cup as Gareth Southgate's side reached the semi-finals, no deal was reached before yesterday's transfer deadline.
Puel said: "We have had good speaking with Harry recently and with the chairman also and we can not change our things just before a game and just before the new season, it is not possible for us".
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Manchester United boss Jose Mourinho made it clear he was keen on bringing at least one defender to the club in the transfer window. He is going to be here for the whole season.
"It's going to be hard away from home at Manchester United, but it's something that we're going to have to be courageous enough to try".
He said: "I was happy with the progress of Harry in the second half of last season".
"We've learnt from the past that, if he takes too many players on like he did at Chelsea and Real Madrid, then there's only one thing that will happen".
Both players were in action on Friday night as Leicester opened their season with a 2-1 defeat to United at Old Trafford, and Chilwell also paid tribute to his teammate's performance.